How do you subtract #\frac { 5a - 2b } { 8a } - \frac { a - 5b } { 8a }#?

1 Answer
smendyka
Aug 1, 2017

See a solution process below:

Explanation:

Because both fractions have the same denominator, we can subtract the numerators over the common denominator:

#(5a - 2b)/(8a) - (a - 5b)/(8a)#

#((5a - 2b) - (a - 5b))/(8a)#

We can remove the terms from their parenthesis being careful to manage the signs of the individual terms correctly:

#(5a - 2b - a + 5b)/(8a)#

Next, we can group the like terms in the numerator:

#(5a - a - 2b + 5b)/(8a)#

Now, we can combine like terms in the numerator:

#(5a - 1a - 2b + 5b)/(8a)#

#((5 - 1)a + (-2 + 5)b)/(8a)#

#(4a + 3b)/(8a)#

If necessary, we can separate the fractions as:

#(4a)/(8a) + (3b)/(8a)#

#(color(red)(cancel(color(black)(4)))color(blue)(cancel(color(black)(a))))/(color(red)(cancel(color(black)(8)))2color(blue)(cancel(color(black)(a)))) + (3b)/(8a)#

#1/2 + (3b)/(8a)#

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